Method for improving clinical data quality in positron emission tomography

ABSTRACT

A method for improving clinical data quality in Positron Emission Tomography (PET). The method provides for the processing of PET data to accurately and efficiently determine a data signal-to-noise ratio (SNR) corresponding to each individual clinical patient scan, as a function of a singles rate in a PET scanner. The method relates an injected dose to the singles rate to determine SNR(D inj ), and provides an accurate estimate of a quantity proportional to SNR, similar in function to the SNR(D inj ). Knowledge of SNR(D inj ) permits determination of peak SNR, optimal dose, SNR deficit, dose deficit, and differential dose benefit. The patient dose is fractionated, with a small calibration dose given initially. After a short uptake, the patient is pre-scanned to determine T, S, and R. An optimal dose is then determined and the remainder injected.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No.60/520,029, filed Nov. 14, 2003.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not Applicable

BACKGROUND OF THE INVENTION

1. Field of Invention

The present invention pertains to the field of Positron EmissionTomography (PET). More particularly, this invention relates to a methodfor improving the quality of clinical data in PET.

2. Description of the Related Art

The statistical precision of PET coincidence data is characterized byits signal-to-noise ratio (SNR), which is defined as the ratio of themean N of the data to its root mean square (standard) deviation σ. Usingthe approximation that the deviations of the true, random and scatteredcoincidences from their respective mean values are uncorrelated andPoisson distributed, and assuming that a noiseless estimate of the meanof the scatter is available, the SNR of the scatter- andrandoms-corrected coincidence data can be expressed as:

${{SNR} = {\frac{N}{\sigma} = {{( \frac{T^{2}}{T + S + {kR}} )^{1/2}t^{1/2}} = {{NECR}^{1/2}t^{1/2}}}}},$where T is the rate of true coincidences detected, S is the scatter, andR is the randoms. k is a constant between 1 and 2 depending on thevariance of the randoms estimate, where k=1 for no noise and k=2 forvariance equal to the mean. t is the duration of the acquisition. Thequantity

$\frac{T^{2}}{T + S + {kR}}$represents the noise equivalent count rate (NECR). These count rates mayeither be global or refer to spatially localized regions of the datathat correspond to specific regions of interest in the object beingimaged. See R. H. Huesman, “A new fast algorithm for the evaluation ofregions of interest and statistical uncertainty in computed tomography,”Phys. Med. Biol., vol. 29, pp. 543-552 (1984).

The National Electrical Manufactures Association (NEMA) has defined NECRas a standard for quantifying the count rate performance of PETscanners. See, for example, National Electrical ManufacturesAssociation, Rosslyn, Va., NEMA Standards Publication NU 2-2001,Performance Measurements of Positron Emission Tomographs,(2001); M. E.Daube-Witherspoon, et al., “PET performance measurements using the NEMANU 2-2001 standard,” J. Nucl. Med., vol. 43, pp. 1398-1409 (October2002); and S. C. Strother, et al., “Measuring PET scanner sensitivity:Relating countrates to image signal-to-noise ratios using noiseequivalent counts,” IEEE Trans. Nuc. Sci., vol. 37, pp. 783-788 (April1990). The standard measurement is performed on a 20 cm diameter, 70 cmlong phantom and involves accurately estimating the scatter and randomscontribution to the data over an extended activity range. Thismeasurement is intended to roughly approximate conditions of humanwhole-body scans.

Although it quantifies data quality, integral NECR is not necessarily adirect measure of image quality or clinical utility. One reason for thisis that an NECR based on total count rates does not distinguishdiagnostic from physiological regions of activity, the diagnosticregions being of interest. SNR in localized data regions of interestshould be studied in order to make clinically relevant quantitativeestimates. Yet integral NECR is meaningful as a relative criterion forselecting patient acquisition parameters to the extent that the rates ofuseful and extraneous events are simultaneously optimized. While thereare exceptions, it is physically plausible that global optimization isusually worthwhile.

It is useful to characterize clinical data in terms of NECR in order tooptimize parameters such as patient dose, uptake period, and frameduration. However, as a practical matter, estimation of NECR on patientdata is difficult. R. J. Smith et al., “Comparisons of clinicalperformance with standard measures of PET cameras,” 1998 IEEE NSS andMIC Conf. Rec., no. M6-11 (1999), showed a correlation of the promptsand trues rates as a function of singles rates between patient data andstandard phantom measurements, but did not evaluate NECR performance. R.D. Badawi et al., “A simulation-based assessment of the revised NEMANU-2 70-cm long test phantom for PET,” 2001 IEEE NSS and MIC Conf. Rec.,no. M6-6 (2002), compared NEMA 70 cm phantom NECR results to Monte Carlosimulations of three anthropomorphic models on two scanners, employingcomputed information that is not readily available clinically. C.Lartizien et al., “Optimization of injected dose based on noiseequivalent count rates for 2- and 3-dimensional whole-body PET,” J.Nucl. Med., vol. 43, pp. 1268-1278 (September 2002), have also evaluatedpatient data in terms of NECR. However, these studies used measurementson an anthropomorphic phantom to derive models for the prompt anddelayed coincidence rates as a function of singles rates, and did notattempt to fit these models directly to the patient data, relyinginstead on the similarity between the phantom and patients.

Higher SNR implies relatively less noise in the data and is related toimproved image quality. Thus it is desirable to maximize SNR forclinical acquisitions. To do this it is necessary to know the dependenceof SNR on the patient's injected dose D_(inj) of radiopharmaceutical.FIG. 1 illustrates SNR as a function of a patient's injected doseD_(inj) after a 1 hour uptake.

This relation depends on many quantities including the patient's weightand distribution of attenuating tissue, the distribution of the emitterin the body, the region of the body being scanned, the position of thepatient in the scanner, and the uptake period. It also depends onvarious characteristics of the scanner itself, including its shielding,sensitivity, dead time per detected event, and its energy and timediscrimination capabilities. In general, SNR(D_(inj)) is not known forclinical acquisitions. Only the single point illustrated at 12 in FIG.1, corresponding to the actual acquisition, can typically be determined.

Direct measurement of SNR(D_(inj)) on a human subject using the mostimportant radiopharmaceutical, ¹⁸F-FDG, takes several hours, duringwhich the subject must remain motionless. ¹⁸F-FDG has a half-life of109.77 min, and the SNR(D_(inj)) measurement does account for migrationof activity in the body. Therefore, such measurement is not feasible.Measurements made with a different, shorter-lived, radioisotope are notrelevant to FDG due to potential differences in biodistribution.

Attempts have been made to determine SNR(D_(inj)) for patients by usingMonte Carlo simulations and by making measurements on anthropomorphicphantoms. These techniques do not address all characteristics ofparticular patient scans and hence do not provide SNR(D_(inj)) forspecific clinical imaging situations, but only offer general guidance.Further, they are time consuming to perform and hence not clinicallypractical. From the prior art, there is not an efficient, accurate meansof estimating a patient- and scan-specific SNR(D_(inj)), or a quantityproportional to it, from a single clinical measurement.

Once SNR(D_(inj))is known, it can be used to determine how to adjustinjected dose, as well as other scan parameters, to optimize thetradeoffs among data quality, radiation dose to the patient, and scantime.

BRIEF SUMMARY OF THE INVENTION

The present invention is a method for improving clinical data quality inPositron Emission Tomography (PET). In the method of the presentinvention, data is processed to accurately and efficiently determine adata signal-to-noise ratio (SNR) corresponding to each individualclinical patient scan, as a function of a singles rate or similarparameter in a PET scanner. The method of the present invention relatesan injected dose to the singles rate to determine SNR(D_(inj)). Themethod of the present invention further provides an accurate estimate ofa quantity proportional to SNR², the estimate being similar in functionto the SNR(D_(inj)), but being simpler to compute.

The singles rate is measured as a total over many crystals. The deadtime, pile-up and multiplexing losses are fundamentally functions of theblock singles rates. The data quality is characterized in terms ofintegral count rates over the region of interest, the total trues,randoms and singles:

$\begin{matrix}{{T = {\sum\limits_{{ij} \in {ROI}}{w_{ij}t_{ij}}}};} \\{{R = {\sum\limits_{{ij} \in {ROI}}{w_{ij}r_{ij}}}};{and}} \\{{s = {\sum\limits_{i \in {ROI}}s_{i}}},}\end{matrix}$where w_(ij) is a sinogram weighting factor and i and j are sinogram binindexes. T and R are characterized in terms of the integral single rate.For any fixed object position, emitter distribution, and fixed scannerconfiguration, only the strength of the activity varies, and theintegral rates T(s) and R(s) have simple functional forms defined as:T(s)=c ^(T) sƒ ^(T)(s); andR(s)=c ^(R) s ²ƒ^(R)(s),where s represents the total measured singles rate, c^(T) and c^(R) areconstants, and ƒ^(T) and ƒ^(R) are functions that account for datalosses due to dead time, pile-up and multiplexing, but depend verylittle on the nature of the object being scanned. The object dependenceis nearly entirely encapsulated in the scale factors c^(T) and c^(R).ƒ^(T)(s) and ƒ^(R)(s) depend very little on most scanner configurationparameters such as the pulse integration time, the energy discriminatorsettings, and the coincidence time window. ƒ^(T)(s) and ƒ^(R)(s) havesimilar, but not identical shapes.

Count rate models in which the independent variable is the integralsingle event rate of the scanner, s, have been discussed. However,alternative methods exist that serve as the model parameter in place ofs. A measurable quantity is acceptable if it is uniquely related to thetrues and randoms count loss fractions over the range of count rates ofinterest, without regard to the nature of the object being scanned; andif it exhibits a monotonic relation to the amplitude, A, of the activitypresent in the body over this range, for a given, fixed scanconfiguration. For a given parameter p, p may be any directly measuredor derived quantity that is or could be employed to provide a dead timeor count loss correction in a PET tomograph. Such quantities include,for example, the output of a live-time clock, the output of a pulsepropagation circuit, and a quantity derived from the randoms coincidencerate itself. p may be either a scalar or vector quantity, for instance,either the integral singles rate, or a vector representing the singlesrates in each detector. In any of these cases, p may be used in place ofs to model the count rate response in clinical scans.

T(s) and R(s) are measured for a given scanner at one or more values ofs using a phantom. The phantom is selected from a 70 cm long, 20 cmdiameter phantom specified by the NEMA NU 2-2001 standard, ananthropomorphic phantom, or another appropriate distribution. Thediscrete measured values are interpolated or extrapolated using apolynomial or other appropriate function. From a patient measurement ata single activity level, the trues and randoms rates at any singles rateare determined according to:

$\begin{matrix}{{{T_{pat}(s)} = {\frac{T_{pat}( s_{pat}^{meas} )}{T_{phant}( s_{pat}^{meas} )}{T_{phant}(s)}}};{and}} \\{{R_{pat}(s)} = {\frac{R_{pat}( s_{pat}^{meas} )}{R_{phant}( s_{pat}^{meas} )}{{R_{phant}(s)}.}}}\end{matrix}$

The above equations for trues and randoms rates apply whether or notscattered events S are included in T. Therefore:

${( {T + S} )_{pat}(s)} = {\frac{( {T + S} )_{pat}( s_{pat}^{meas} )}{( {T + S} )_{phant}( s_{pat}^{meas} )}( {T + S} )_{phant}{(s).}}$

The scatter fraction S_(f)=S/(T+S) varies only slightly with count rate.As a result, T(s) and (T+S)(s) have nearly the same shape. (T+S) is thenet trues, defined by the difference between the prompt and delayedcoincidences. (T+S) is measured directly, and T is estimated bysubtracting an estimate of the mean scatter distribution. The scattersinogram is determined using a technique such as a simulation algorithm,convolution, curve fitting, or multiple energy windows. For a noisyscatter estimate, such must be accounted for in the computation of theSNR. R is estimated in any of several methods. Namely, R is estimateddirectly from a delayeds sinogram, as a fraction of the total delayedsrate assuming a uniform distribution and using an attenuation mask, orfrom the spatial distribution of the singles rates. Once T. S and R areknown, the SNR is estimated as a function of the singles rate.

Activity in the patient, and therefore injected dose, is related to thesingles rate in a similar manner to the one described above. For a givenobject, the variation of the singles rate with activity departs fromlinearity only due to the dead time in the block analog channels. Aslong as the incident photon flux is reasonably uniform, the dead time issimilar and the activity A as a function of the singles rate depends onthe object only via a scale factor. Therefore, a phantom measurement ofactivity vs. singles is calibrated to a single patient acquisition todetermine the patient's dose response curve:

${{A_{pat}(s)} = {\frac{A_{pat}( s_{pat}^{meas} )}{A_{phant}( s_{pat}^{Meas} )}{A_{phant}(s)}}},$where A represents either a total activity, or a mean activityconcentration per mass or volume.

Over the clinical range, A is a monotonic function of s and consequentlycan be inverted to give s as a function of A_(pat). Therefore theformula for A_(pat)(s) given above is used to relate T, S, and R to A.Injected dose D_(inj) is proportional to A with the proportionalityconstant being the product of a decay factor and an excretion fraction.Therefore D_(inj) may be used instead of A in the equation given forA_(pat)(s) above, since D_(inj) is the directly measured quantity.SNR(D_(inj)) is then determined. Likewise, SNR is determined as afunction of any quantity related to activity, such as uptake period;excretion fraction; and dose fractionation, that is, a dose administeredin several partial doses.

Knowledge of SNR(D_(inj)) permits determination of several quantitiesrelating to data quality. These qualities include peak SNR, optimaldose, SNR deficit, dose deficit, and differential dose benefit. The peakSNR is the maximum SNR that could have been realized for any dose oruptake, neglecting redistribution. Optimal dose is defined as the dosethat would have achieved peak SIWR, all else being the same. The SNRdeficit is the difference or ratio between actual and peak SNR. Dosedeficit is defined as the additional dose needed to achieve peak SNR.Finally, the differential dose benefit is the incremental increase inSNR per unit incremental increase in dose. Alternatively, a value of SNRless than the peak value may be defined as the optimal operationalpoint, for example 90-95% of peak SNR, and the optimal dose may bedefined as the minimum dose needed to achieve this SNR value. Becausethe peak of SNR(D_(inj)) is frequently quite broad, a large reduction ininjected dose results in only a small reduction in SNR.

According to standard clinical protocol a patient is injected withradiopharmaceutical only once and an uptake period must elapse prior toscanning. Thus by the time T. S, and R can be determined by conventionalmethods, it is too late to adjust the dose to improve performance.However, in accordance with the method of the present invention,modified protocols may be employed. Specifically, the dose may befractionated, with a small calibration dose given initially. After ashort uptake, the patient is pre-scanned for a short period timed onlylong enough to determine T. S, and R. The duration of the pre-scan is asshort as a few seconds. From T. S, and R, an optimal dose is determinedand the remainder injected. Calibration is performed by either astandard scanner, or on a special calibration device consisting of asfew as two detectors. Spatial resolution is not necessarily required. Ascan is optimizable for various scanner parameters by employingSNR(D_(inj)) estimates for such parameters. These parameters include,for example, the lower level discriminator setting (LLD).

The optimal dose for one anatomical position in the patient is generallynot the same as for others. Knowledge of SNR(D_(inj)) for each positionpermits a global optimization to be performed. Frequently, individualpatients are scanned multiple times, as for instance when they areundergoing radiation treatment or chemotherapy. In such cases knowledgeof SNR(D_(inj)) acquired in the first scan is useful for optimizingsubsequent scans.

Because optimal SNR occurs within a very narrow range of singles ratesfor a variety of patient weights and anatomical positions, it is onlynecessary to measure the singles rate to get an accurate assessment ofwhether the injected dose was optimal.

In an alternate embodiment of the present invention, noise equivalentcount rate (NECR) is employed as the performance metric, as opposed toSNR. Where the scatter and randoms fractions are not known, pseudo-NECR(PNECR) is also useful. PNECR has a dependence on the singles ratesimilar to NECR, but does not account for differences in scatterfractions among different objects. Accordingly, PNECR is not useful forgiving an absolute estimate of differences in performance betweenobjects. Nevertheless, PNECR is useful for determining the optimal doseand the performance deficit ratio for a given scan, as well as adifferential dose benefit.

In the alternate method for analyzing clinical PET count rateperformance using NECR, net trues (prompts—delayeds) and randoms(delayeds) count rate responses measured on a reference phantom arematched to the actual patient data. An estimated response curve is thenused to compute a performance metric closely related to the NECR as afunction of the total singles event rate in the system. From this, thepeak performance value relative to the measured performance isdetermined for any individual acquisition. This maximum performancevalue is largely independent of the magnitude of the activity present inthe patient at the time of the acquisition, but depends mainly on theemitter and attenuator distributions. The peak count rates are then usedto derive frame durations for equivalent noise, and correlated withpatient weight. The singles rate is also determined. From the singlesrate, the activity necessary to achieve maximum performance isdetermined and, based on the known activity in the patient, the optimalinjected dose is determined.

Expressed in terms of the total (scatter corrected) trues (T), randoms(R) and scatter (S) count rates, the integral Poisson noise equivalentcount rate (NECR) for the scatter and randoms corrected measured data isexpressed as:

${NECR} = {\frac{T^{2}}{T + S + {kR}} = {\frac{( {P - D} )^{2}( {1 - S_{f}^{tot}} )^{2}}{P + {( {k - 1} )D} - S_{out} - {kR}_{out}}.}}$

Here, k=2 for online randoms subtraction and 1 when a smooth randomsestimate is employed. R and S include counts only from LORs passingthrough the patient. P is the total prompts rate, D is the total countrate in a delayed coincidence window, and S_(out) and R_(out) arerespectively the scatter and randoms events that lie outside of thepatient.

S_(f)^(tot) = (S + S_(out))/(P − D)is the total scatter fraction. Typically, S_(out) is a small fraction ofthe net trues (P−D)—about 15% for a 20 cm diameter cylinder, and lessfor patients. An average patient's thorax and abdomen subtendapproximately 47% of the sinogram for a full ring scanner of the typeconsidered here. If the randoms are uniformly distributed, then2R_(out)≈D. NECR is therefore approximated by:

${NECR} \approx {( {1 - S_{f}^{tot}} )^{2}{\frac{( {P - D} )^{2}}{P + {( {{k/2} - 1} )D}}.}}$

The prefactor affects the scale of the NECR, but not the relativeperformance of two scans of objects having similar scatter fractions.Thus the prefactor is dropped and a pseudo-NECR (PNECR) metric isdefined for evaluating the effects of dose, uptake and frame duration ondata quality for a specific object:

${PNECR} \equiv {\frac{( {P - D} )^{2}}{P + {( {{k/2} - 1} )D}}.}$PNECR, unlike NECR, is easily computed from the total prompt and delayedcoincidence event rates without explicit knowledge of the scatter andrandoms within the patient. If online randoms subtraction is used forrandoms correction, so that k=2, then the denominator (P+(k/2−1)D) issimply P.

The net trues (P−D) and delayeds (D) count rate curves are modeled asfunctions of singles rate in the same manner as described for (T+S) andR, and are fit to the patient data by simple scaling. From this,PNECR(s) is computed. A continuous representation of the model curves of(P−D) and D may be obtained by fitting appropriate functional forms tothe phantom data. PNECR(s) is computed for each bed position for whichthe coincidence rates are evaluated at the patient's singles rate. Theactual measured PNECR point will fall on this curve, and its deficitrelative to the peak PNECR value is then determined. Since for a singlepatient and bed position the scatter fraction is fixed, the ratio ofactual to peak PNECR accurately reflects the NECR deficit as well.Further, the peak PNECR, unlike the measured PNECR, is largelyindependent of the activity present in the patient, and hence of thedose and uptake period. Accordingly, the peak PNECR is also a usefulquantity to correlate with other factors, such as patient weight, thataffect data quality.

Knowing the peak singles rate, defined as the singles rate at the peakPNECR, compared to the measured singles rate, the difference in theactivity present in the patient that would have been necessary toachieve peak performance is predicted. The transformation from singlesrate to activity is based on the reference phantom scan. That ratio ofactivity A in the phantom at the patient's peak singles rate to thephantom activity at the measured singles rate in the patient gives acorrection factor for the patient's activity as:

$\frac{A_{peak}^{patient}}{A_{actual}^{patient}} = {\frac{A^{phantom}( s_{peak}^{patient} )}{A^{phantom}( s_{actual}^{patient} )}.}$

This activity ratio, as in the case using SNR(D_(inj)) described above,is applied to the actual injected dose to predict the optimal dose. Theoptimal dose is then decay corrected to a standard uptake period such asone hour. The optimal dose is not sensitive to the elimination of partof dose, so long as the eliminated fraction remains constant.

Based on knowledge of the singles rate at the peak PNECR, the ratio ofthe patient's activity at the time of the scan to that which would havebeen required to achieve maximum performance is estimated.

A means of determining SNR(s), NECR(s) or PNECR(s) for each individualscan of a patient population is described. Alternatively such apopulation may be represented by average SNR(s), NECR(s) or PNECR(s)curves determined in a number of ways, for example, by using a leastsquares algorithm to fit the scaling parameters of the average responsecurves to the patient data.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

The above-mentioned features of the invention will become more clearlyunderstood from the following detailed description of the invention readtogether with the drawings in which:

FIG. 1 is a graphical illustration of the signal-to-noise ratio of PETcoincidence data as a function of a patient's injected dose D_(inj)after a 1 hour uptake;

FIG. 2 is a graphical illustration of peak SNR, optimal dose, SNRdeficit, dose deficit, and differential dose benefit, each related todata quality and optimization;

FIG. 3 is a graphical illustration of the correlation between singlescount rate and activity for patients acquired with a PET/CT scannerhaving BGO scintillators and NEMA 70 cm phantom data;

FIG. 4 is a graphical illustration of the correlation between activityconcentrations for BGO PET/CT patient and NEMA 70 cm phantom data, withthe equivalent phantom activities being estimated from the singles ratesobserved in the patients;

FIG. 5 illustrates a first phantom arrangement wherein a water-filledphantom having a diameter of 21 cm and a length of 23 cm is employed;

FIG. 6 illustrates a second phantom arrangement wherein a polyethylenephantom having a diameter of 20 cm diameter, a length of 70 cm, and aweight of approximately 22 kg. is employed;

FIG. 7 illustrates a third phantom arrangement wherein two NEMA 70 cmphantoms and one water-filled phantom having a 21 cm diameter and alength of 70 cm long is employed;

FIG. 8 illustrates a comparison between PNECR and NECR for NEMA 70 cmphantom count rate data acquired on four PET and PET/CT scanners;

FIG. 9 illustrates a comparison of PNECR and NECR for acquisitions usingthe three different phantom arrangements of FIGS. 5-7, all acquisitionsbeing made on an LSO PET/CT scanner;

FIG. 10 illustrates a comparison between P. (P−D) and D for the threephantom count rate studies on the LSO PET/CT scanner illustrated in FIG.9;

FIG. 11 illustrates a comparison of net trues and delayeds count ratesmeasured for 93 bed positions in 15 patient studies on an ACCEL, withthe fitted model curves from a NEMA 2001 count rate test;

FIG. 12 illustrates an average PNECR predicted for the data setillustrated in FIG. 11, together with the actual PNECR for each bedposition, and the PNECR curve for the NEMA 2001 reference phantom;

FIG. 13 illustrates the actual and average patient PNECR of a set of 17clinical whole-body studies comprising 84 bed positions on a BGO PET/CTscanner;

FIG. 14 illustrates the computed maximum value of each individual PNECRcurve as a function of patient's weight;

FIG. 15 illustrates an estimated scan duration, based on the trend ofpeak PNECR count rate versus weight illustrated in FIG. 14, to acquirean equal number of pseudo-noise equivalent counts at each weight, whichis proportional to the reciprocal of the count rate, and normalized tounit scan time at 70 kg;

FIG. 16 illustrates the ratio of actual to maximum PNECR for individualacquisitions versus patient weight;

FIG. 17 illustrates an estimate of the ratio of the patient's activityat the time of the scan to that which would have been required toachieve maximum performance; and

FIG. 18 illustrates predicted doses of ¹⁸F-FDG that would have beenrequired to achieve the peak count rate, based on the activity ratiosillustrated in FIG. 17, the predicted doses being decay corrected to anhour prior to each individual acquisition.

DETAILED DESCRIPTION OF THE INVENTION

A method for improving clinical data quality in Positron EmissionTomography (PET) is disclosed. In the method of the present invention,data is processed to accurately and efficiently determine a datasignal-to-noise ratio (SNR) corresponding to each individual clinicalpatient scan, as a function of a singles rate in a PET scanner. Themethod of the present invention relates an injected dose D_(inj) to thesingles rate to determine SNR(D_(inj)). The method of the presentinvention further provides an accurate estimate of a quantityproportional to SNR, the estimate being similar in function to theSNR(D_(inj)), but being simpler to compute. The method of the presentinvention has several applications for assessment and optimization ofclinical PET data quality.

The single photon event rate in a detector channel depends on severalfactors. Among these are the activity α in the patient, the solid angleof the detector for the emitted radiation, the attenuation of theradiation between the emission point and the detector, the efficiency ofthe detector for the incident photon, and the loss probability of theevent due to dead time and pile-up in the detector. Of these factors,the dead time and pile-up depend on the incident event rate. Themeasured true and random coincidence rates depend on all of thesefactors, as well as losses in the multiplexors that compress the signalsbetween the detectors and the coincidence processor. Multiplexing lossesalso depend on event rate. Singles do not experience multiplexing losseson PET scanners in which they are counted at the input of themultiplexors, such as those manufactured by CTI Pet Systems, Inc. (CPS),Knoxville, Tenn. For a pair of detectors, i and j, these relations areexpressed as:s _(i) =d _(i)(α)ε_(i)α;s _(j) =d _(j)(α)ε_(j)α;t _(ij) =[d _(i)(α)m _(i)(α)ε_(i) α]d _(j)(α)m _(j)(α)ε_(ji); andr _(ij) =[d _(i)(α)m _(i)(α)ε_(i) α]└d _(j)(α)m _(j)(α)ε_(j)┘2τ,where s, t, and r are the singles, trues and randoms rates,respectively, d and m are the dead time/pile-up and multiplexing lossfunctions, respectively, and τ is coincidence resolving time. Therandoms rate may also include a small contribution from multiple events,depending on the design of the system. However, such contribution isnegligible in the present method.

ε_(i) is a factor which includes the solid angle, attenuation anddetector efficiency. ε_(ji) is the probability that a photon willinteract in detector j given that its annihilation partner is detectedin i. ε_(i) and ε_(ji) depend on the distribution of the activity butnot its magnitude, so they are not count rate dependent. Over theclinical range of activity, s is a monotonically increasing function ofα. Therefore t and r are expressed as functions of the appropriatesingles rates:t _(ij)=ε_(ji) d _(j)(s _(j))m _(i)(s _(i))m _(j)(s _(j))s _(i); andr _(ij)=2τm _(i)(s _(i))m _(j)(s _(j))s _(i) s _(j).

With this, nearly all of the dependence on the object (due to variationsin ε_(i)) has been absorbed into the measured singles rates. Themultiplexing loss depends on the singles rates in all of the inputchannels, so an object dependent change in the distribution of theserates could minimally affect m_(i)s_(i). Thus r_(ij)(s_(i), s_(j)) isessentially independent of the object, while t_(ij)(s_(i), s_(j))depends on it only through the scalar factor ε_(ji). Therefore, bymeasuring r_(ij) and t_(ij) as functions of the singles rates on aphantom, the corresponding functions for a patient are inferred byscaling the measured curves to patient data acquired at a singleactivity level, thereby determining the scale factors.

The above analysis is somewhat idealized in that the singles rate onmost scanners is not measured for each individual crystal. In practice,the singles rate is measured as a total over many crystals. On the aboveexemplary CPS scanners, for example, singles rates are recorded astotals over three or four block detectors, each typically including 64crystals. The dead time, pile-up and multiplexing losses arefundamentally functions of the block singles rates. However, as long asthe singles rates are reasonably uniform over these block channels, ormore generally, if the distribution of singles does not vary appreciablyover this group of three or four blocks for different objects, then theanalysis is also valid when applied to these integral rates.

The above description is applicable to individual lines of response(LORs). However, typically of interest is the characterization of dataquality of a region of the sinogram, including a portion of the datavolume, or the entire data volume. The data quality is characterized interms of integral count rates over the region of interest, the totaltrues, randoms and singles:

$\begin{matrix}{{T = {\sum\limits_{{ij} \in {ROI}}{w_{ij}t_{ij}}}};} \\{{R = {\sum\limits_{{ij} \in {ROI}}{w_{ij}r_{ij}}}};{and}} \\{{s = {\sum\limits_{i \in {ROI}}s_{i}}},}\end{matrix}$where w_(ij) is a sinogram weighting factor that may be definedsimilarly to those described by R. H. Huesman, id.

T and R are characterized in terms of the integral single rate. Ingeneral, T and R are not singled valued functions of s where largevariations exist in the distribution of the singles among the variouschannels for different objects, due to the non-linear dependence of theloss functions on the channel count rates. However, in clinical imaging,the distribution of singles events among the detector channels tends tobe fairly uniform, with a variation of less than a factor of two. Theinclusion of many channels, as for instance when the total counts in thesinogram are considered, tends to average out differences among the deadtime, pile-up and multiplexing losses. Therefore, for any fixed objectposition, emitter distribution, and fixed scanner configuration, onlythe strength of the activity varies, and the integral rates T(s) andR(s) have simple functional forms defined as:T(s)=c ^(T) sƒ ^(T)(s); andR(s)=c ^(R) s ²ƒ^(R)(s).where s represents the total measured singles rate, c^(T) and c^(R) areconstants, and ƒ^(T) and ƒ^(R) are functions that account for datalosses due to dead time, pile-up and multiplexing, but depend verylittle on the nature of the object being scanned. The object dependenceis nearly entirely encapsulated in the scale factors c^(T) and c^(R).These results have been validated through a set of phantom measurementsas described below. ƒ^(T)(s) and ƒ^(R)(s) depend very little on mostscanner configuration parameters such as the pulse integration time, theenergy discriminator settings, and the coincidence time window. ƒ^(T)(s)and ƒ^(R)(s) have similar, but not identical shapes.

Count rate models in which the independent variable is the integralsingle event rate of the scanner, s, have been discussed. However,alternative methods exist that serve as the model parameter in place ofs. A measurable quantity is acceptable if it is uniquely related to thetrues and randoms count loss fractions over the range of count rates ofinterest, without regard to the nature of the object being scanned; andif it exhibits a monotonic relation to the amplitude, A, of the activitypresent in the body over this range, for a given, fixed scanconfiguration. For parameter p, these criteria are equivalent to thelive times ƒ^(T)(p) and ƒ^(R)(p) being well defined functions of p thatare independent of the scanned object, and that p(A) measured for aphantom is invertible to give A(p).

In general, p may be any directly measured or derived quantity that isor could be employed to provide a dead time or count loss correction ina PET tomograph. Such quantities include, for example, the output of alive-time clock, the output of a pulse propagation circuit, and aquantity derived from the randoms coincidence rate itself. p may beeither a scalar or vector quantity, for instance, either the integralsingles rate, or a vector representing the singles rates in eachdetector. In any of these cases, p may be used in place of s to modelthe count rate response in clinical scans.

T(s) and R(s) are measured for a given scanner at one or more values ofs using a phantom. The phantom is selected from a 70 cm long, 20 cmdiameter phantom specified by the NEMA NU 2-2001 standard, ananthropomorphic phantom, or another appropriate distribution. Thediscrete measured values are interpolated or extrapolated using apolynomial or other appropriate function. From a patient measurement ata single activity level, the trues and randoms rates at any singles rateare determined according to:

$\begin{matrix}{{{T_{pat}(s)} = {\frac{T_{pat}( s_{pat}^{meas} )}{T_{phant}( s_{pat}^{meas} )}{T_{phant}(s)}}};{and}} \\{{R_{pat}(s)} = {\frac{R_{pat}( s_{pat}^{meas} )}{R_{phant}( s_{pat}^{meas} )}{{R_{phant}(s)}.}}}\end{matrix}$

The above equations for trues and randoms rates apply whether or notscattered events S are included in T. Therefore:

${( {T + S} )_{pat}(s)} = {\frac{( {T + S} )_{pat}( s_{pat}^{meas} )}{( {T + S} )_{phant}( s_{pat}^{meas} )}( {T + S} )_{phant}{(s).}}$

The scatter fraction S_(f)=S/(T+S) varies only slightly with count rate.As a result, T(s) and (T+S)(s) have nearly the same shape. (T+S) is thenet trues, defined by the difference between the prompt and delayedcoincidences.

Depending on the application, the scatter and randoms rates refer toeither the total field of view (FOV), or to lines of response (LORs)passing through a region of interest, such as the body. The randoms ratemay or may not include multiple events, depending on the architecture ofthe scanner's coincidence processor. The single photon rate is measuredeither before or after multiplexing losses.

(T+S) is measured directly, and T is estimated by subtracting anestimate of the mean scatter distribution. The scatter sinogram isdetermined using a technique such as a simulation algorithm,convolution, curve fitting, or multiple energy windows. For a noisyscatter estimate, such must be accounted for in the computation of theSNR. R is estimated in any of several methods. Namely, R is estimateddirectly from a delayeds sinogram, as a fraction of the total delayedsrate assuming a uniform distribution and using an attenuation mask, orfrom the spatial distribution of the singles rates. Once T, S and R areknown, the SLVR is estimated as a function of the singles rate.

Activity in the patient, and therefore injected dose, is related to thesingles rate in a similar manner to the one described above. For a givenobject, the variation of the singles rate with activity departs fromlinearity only due to the dead time in the block analog channels. Aslong as the incident photon flux is reasonably uniform, the dead time issimilar and the activity A as a function of the singles rate depends onthe object only via a scale factor. Therefore, a phantom measurement ofactivity vs. singles is calibrated to a single patient acquisition todetermine the patient's dose response curve:

${{A_{pat}(s)} = {\frac{A_{pat}( s_{pat}^{meas} )}{A_{phant}( s_{pat}^{Meas} )}{A_{phant}(s)}}},$where A represents either a total activity, or a mean activityconcentration per mass or volume.

Over the clinical range, A is a monotonic function of s and consequentlycan be inverted to give s as a function of A_(pat). Therefore theformula for A_(pat)(s) given above is used to relate T, S, and R to A.Injected dose D_(inj) is proportional to A with the proportionalityconstant being the product of a decay factor and an excretion fraction.Therefore D_(inj) may be used instead of A in the equation given forA_(pat)(s) above, since D_(inj) is the directly measured quantity.SNR(D_(inj)) is then determined. Likewise, SNR is determined as afunction of any quantity related to activity, such as uptake period;excretion fraction; and dose fractionation, that is, a dose administeredin several partial doses.

Knowledge of SNR(D_(inj)) permits determination of several quantitiesrelating to data quality. These qualities include peak SNR, optimaldose, SNR deficit, dose deficit, and differential dose benefit. The peakSNR is the maximum SNR that could have been realized for any dose oruptake, neglecting redistribution. Optimal dose is defined as the dosethat would have achieved peak SNR, all else being the same. The SNRdeficit is the difference or ratio between actual and peak SNR. Dosedeficit is defined as the additional dose needed to achieve peak SNR.Finally, the differential dose benefit is the incremental increase inSNR per unit incremental increase in dose. Each of these quantities isillustrated in FIG. 2, which graphically depicts the extraction ofquantities related to data quality and optimization. Alternatively, avalue of SNR less than the peak value may be defined as the optimaloperational point, for example 90-95% of peak SNR; and the optimal dosemay be defined as the minimum dose needed to achieve this SNR value.Because the peak of SNR(D_(inj)) is frequently quite broad, a largereduction in injected dose results in only a small reduction in SNR.

According to standard clinical protocol a patient is injected withradiopharmaceutical only once and an uptake period must elapse prior toscanning. Thus by the time T, S, and R can be determined by conventionalmethods, it is too late to adjust the dose to improve performance.However, in accordance with the method of the present invention,modified protocols may be employed. Specifically, the dose may befractionated, with a small calibration dose given initially. After ashort uptake, the patient is pre-scanned for a short period timed onlylong enough to determine T, S, and R. The duration of this pre-scan isas short as a few seconds. From T, S, and R, an optimal dose isdetermined and the remainder injected. Calibration is performed byeither a standard scanner, or on a special calibration device consistingof as few as two detectors. Spatial resolution is not necessarilyrequired. A scan is optimizable for various scanner parameters byemploying SNR(D_(inj)) estimates for such parameters. These parametersinclude, for example, LLD.

The optimal dose for one anatomical position in the patient is generallynot the same as for others. Knowledge of SNR(D_(inj)) for each positionpermits a global optimization to be performed. Frequently, individualpatients are scanned multiple times, as for instance when they areundergoing radiation treatment or chemotherapy. In such cases knowledgeof SNR(D_(inj)) acquired in the first scan is useful for optimizingsubsequent scans.

Because optimal SNR occurs within a very narrow range of singles ratesfor a variety of patient weights and anatomical positions, it is onlynecessary to measure the singles rate to get an accurate assessment ofwhether the injected dose was optimal.

One important use of the method of the present invention is for qualityassurance during a patient scan. It is a goal to scan a patient at orclose to the optimal SNR. Determination of SNR(D_(inj)), and the SNRdeficit, permit an assessment of the scan relative to this goal.Occasionally, due to unforeseen circumstances, a patient cannot be givena desired dose, or scanning is delayed beyond the desired uptake period.In such situations, the method of the present invention allows for theevaluation of the loss of data quality to assess the need for remedialaction such as a repeat scan.

The method of the present invention is also useful as a quality check onthe scanner itself. A single measurement on a standard phantom is usedto generate an SNR(A) curve, which is compared to previous results todetect drifts or significant changes in scanner performance. This iseasily incorporated into the current daily detector check performed onmost PET scanners.

According to the method of the present invention, databases aredeveloped relating patient characteristics such as weight, body massindex (BMI), sex, disease, diabetes state, anatomical position, andothers to optimal dose, peak SNR and other data quality metrics. This isat best extremely difficult to perform without the ability to predictSNR(D_(inj)) on a per scan basis. While one could estimate a single SNRvalue for each scan, it would not be known whether the results couldhave been improved with a different dose. Using prior methods, a largenumber of repeat scans of nearly identical patients at many differentdoses and for each set of patient characteristics is required to achieveinformation similar to SNR(D_(inj)), which is not practical.

Using the method of the present invention, the optimal dose is known foreach scan completed and is statistically correlated via the databasewith important patient characteristics such as weight. From thedatabase, a quantitative estimate of optimal dose for new patients ismade. Using prior methods, the relation between optimal dose and patientweight is not well understood. In some instances, the dose is increasedfor heavier patients, while in others it is not. The method of thepresent invention permits a rapid development of a definite answer tothis protocol issue. For example, the method of the present inventionhas shown that the optimal dose depends very weakly on patient weight,at least on average, suggesting that protocols can accommodate the lowerSNR of heavier patients only by increasing scan time.

It is foreseen that multiple sites can share data collected using themethod of the present invention to improve statistics. A softwareinterface allows an optimal dose and scan time to be determined byentering a patient's characteristics such as weight, and causing theoptimal dose and SNR distributions for all similar patients to bedisplayed.

Given knowledge of SNR for each bed position, scan times are adjusted toequalize SNR across the body, subject to constraints such as total scantime. For continuous bed motion, bed speed is adjusted appropriately fordifferent anatomical regions.

In one use of the method of the present invention, a SNR based on atleast one local ROI as opposed to a global, integral SNR is employed.When a region of interest in an image is determined, the region ismathematically projected into the associated sinogram(s), and the dataassociated with this region is appropriately weighted, selected and usedto estimate a local SNR(D_(inj)).

In an alternate embodiment of the present invention, noise equivalentcount rate (NECR) is employed as the performance metric, as opposed toSNR. Where the scatter and randoms fractions are not known, pseudo-NECR(PNECR) is also useful. PNECR has a dependence on the singles ratesimilar to NECR, but does not account for differences in scatterfractions among different objects. Accordingly, PNECR is not as usefulas NECR for giving an absolute estimate of differences in performancebetween objects. Nevertheless, PNECR is useful for determining theoptimal dose and the performance deficit ratio for a given scan, as wellas a differential dose benefit.

In the alternate method for analyzing clinical PET count rateperformance using NECR, net trues (prompts—delayeds) and randoms(delayeds) count rate responses measured on a reference phantom arematched to the actual patient data. An estimated response curve is thenused to compute a performance metric closely related to the NECR as afunction of the total singles event rate in the system. From this, thepeak performance value relative to the measured performance isdetermined for any individual acquisition. This maximum performancevalue is largely independent of the magnitude of the activity present inthe patient at the time of the acquisition, but depends mainly on theemitter and attenuator distributions. The peak count rates are then usedto derive frame durations for equivalent noise, and correlated withpatient weight. The singles rate is also determined. From the singlesrate, the activity necessary to achieve maximum performance isdetermined and, based on the known activity in the patient, the optimalinjected dose is determined.

Coincidence count rates are analyzed in terms of the total energyqualified singles rates in the detectors. Contrary to the expectationthat the mean activity is well-correlated with the singles rate, asillustrated in FIG. 3 for individual multi-bed whole-body patientstudies, it is not. FIG. 3 is a graphical illustration of thecorrelation between singles count rate and activity for patientsacquired with a PET/CT scanner having BGO scintillators, and alsoincludes NEMA 70 cm phantom data for the scanner. The activities aretotal activity in the phantom or patient at the time of the scan,averaged over the frame duration. The patient activities are based oninjected dose and uptake period, with no correction for possibleexcretion. It can be seen that the total estimated activity in thepatient, not allowing for urinary excretion of part of the dose, must behigher in a typical body than in the phantom to produce equivalentsingles rates. This is likely due to the greater extent and attenuationof the body, as well as excretion.

For several of these studies the singles first increases then decreasesas the total activity in the patient decreases, giving rise to a“boomerang” shaped trend, as shown at 14 for one patient study in FIG.3. This is due to the motion of the bed to scan different regions of thebody with varying concentrations of activity. Differences in patientweight can also lead to variation in singles rates for a given amount ofactivity present, due to differences in radiation absorption. Analysisin terms of the singles rates removes these first order effects of theemitter and attenuator distributions.

In the prior art, phantom performance results are related to patients byestimating an activity concentration in the patient, computed bydividing her total activity by her weight, and comparing this to theactivity concentration in the phantom. In the method of the presentinvention, the patient and phantom data are compared at equivalentsingles rates. As a result, the corresponding activity concentration inthe phantom is significantly different from that in some patients. Thisis shown in FIG. 4 for the NEMA 70 cm phantom and the BGO PET/CT, wherethe equivalent phantom activities have been computed for each patientsingles rate according to the trend seen in FIG. 3. FIG. 4 is agraphical illustration of the correlation between activityconcentrations for BGO PET/C^(T) patient and NEMA 70 cm phantom data,with the equivalent phantom activities being estimated from the singlesrates observed in the patients. The patient activities are based oninjected dose and uptake period, with no correction for possibleelimination. A linear regression through the data is shown, with slope0.52. For this patient sample, the equivalent phantom activityconcentration is on average about twice the patient's activity, or evengreater considering the possible elimination of radioactivity from thepatient that may have occurred. Care must therefore be taken whencomparing phantom and patient count rate performance based on activity.This could imply very different photon flux environments. It ispreferable to eliminate this object-dependent variability from theanalysis.

Expressed in terms of the total (scatter corrected) trues (T), randoms(R) and scatter (S) count rates, the integral Poisson noise equivalentcount rate (NECR) for the scatter and randoms corrected measured data isexpressed as:

${NECR} = {\frac{T^{2}}{T + S + {kR}} = {\frac{( {P - D} )^{2}( {1 - S_{f}^{tot}} )^{2}}{P + {( {k - 1} )D} - S_{out} - {kR}_{out}}.}}$

Here, k=2 for online randoms subtraction and 1 when a smooth randomsestimate is employed. R and S include counts only from LORs passingthrough the patient. P is the total prompts rate, D is the total countrate in a delayed coincidence window, and S_(out) and R_(out) arerespectively the scatter and randoms events that lie outside of thepatient.

S_(f)^(tot) = (S + S_(out))/(P − D)is the total scatter fraction. Note that P−D=T+S+S_(out). Typically,S_(out) is a small fraction of the net trues (P−D)—about 15% for a 20 cmdiameter cylinder, and less for patients. An average patient's thoraxand abdomen subtend approximately 47% of the sinogram for a full ringscanner of the type considered here. If the randoms are uniformlydistributed, then 2R_(out)≈D. NECR is therefore approximated by:

${NECR} \approx {( {1 - S_{f}^{tot}} )^{2}{\frac{( {P - D} )^{2}}{P + {( {{k/2} - 1} )D}}.}}$

The prefactor affects the scale of the NECR, but not the relativeperformance of two scans of objects having similar scatter fractions.Thus the prefactor is dropped and a pseudo-NECR (PNECR) metric isdefined for evaluating the effects of dose, uptake and frame duration ondata quality for a specific object:

${PNECR} \equiv {\frac{( {P - D} )^{2}}{P + {( {{k/2} - 1} )D}}.}$

PNECR, unlike NECR, is easily computed from the total prompt and delayedcoincidence event rates without explicit knowledge of the scatter andrandoms within the patient. If online randoms subtraction is used forrandoms correction, so that k=2, then the denominator (P+(k/2−1)D) issimply P.

It should be noted that the NEMA prescription for computing NECR usingthe 70 cm phantom cannot be followed on the LSO-based scanners discussedhere due to the intrinsic background from the natural radioactivity of¹⁷⁶Lu. The randoms rate never falls below 1% of the trues rate. Toobtain an accurate NECR estimate on these machines, both a prompts anddelayeds sinogram are acquired and the actual randoms within the 24 cmregion of interest specified by NEMA are computed, rather thanestimating them based on the measured trues and scatter fraction. Thisis a more exact procedure than the NEMA standard, and also accounts forthe slight variation in scatter fraction observed as a function ofactivity.

To validate the use of PNECR as a relative performance measure, PNECR totrue NECR have been compared on data from the three phantom arrangementsshown in FIGS. 5-7. Illustrated in FIG. 5 is a phantom 16A having adiameter of 21 cm and a length of 23 cm. The phantom 16A in a uniformwater-filled cylinder having an active volume of 20 cm diameter by 20 cmlong and a weight of 6.5 kg. Illustrated in FIG. 6 is a phantom 16Bhaving a diameter of 20 cm diameter, a length of 70 cm, and a weight ofapproximately 22 kg. The phantom 16B is fabricated from polyethylenephantom with a 22 kg line source as specified by NEMA. The thirdconfiguration, as illustrated in FIG. 7, includes two phantoms 16D, 16E,which are NEMA 70 cm phantoms, and a water-filled phantom 16C having a21 cm diameter and a length of 70 cm long. The phantom 16D, disposed onthe top of the illustrated stack, contains a standard NEMA line source.The lower two phantoms 16C, 16E contain no radioactivity. The totalweight of the phantoms 16C, 16D, 16E is approximately 70 kg.

FIG. 8 illustrates a comparison between PNECR and NECR for NEMA 70 cmphantom count rate data acquired on four CPS Innovations PET and PET/CTscanners. These scanners included the EXACT HR+, the ACCEL, the BGOPET/CT and the LSO PET/CT tomographs. The HR+ and the BGO PET/C^(T) bothcontain 288 BGO block detectors each of dimension 36×38.8×30 mm. TheACCEL and the LSO PET/C^(T) both contain 144 LSO block detectors each ofdimension 54×54×25 mm. All four scanners employed a lower leveldiscriminator setting of 350 keV. All acquisitions were 3D with onlinerandoms subtraction. The scale factors were 0.23-0.26. The dashed linesare PNECR values. The PNECR curves have been scaled to match the NECRvalues. FIG. 9 illustrates a comparison of PNECR and NECR foracquisitions using the three different phantoms, all on the LSO PET/CT.Scale factors of 0.40, 0.26 and 0.17 were used for the phantomsillustrated in FIGS. 5-7, respectively. In all cases illustrated inFIGS. 8 and 9, the shape of the PNECR curve closely resembles the actualNECR curve. Accordingly, the relative performance of clinicalacquisitions using PNECR is evaluated.

In order to understand the count rate performance for a given patientand bed position study, the corresponding NECR or PNECR as a function ofsingles are desired. However, it is not practical to measure clinicallydue to the time required. Thus, PNECR is estimated as a function ofsingles for a patient study by fitting the net trues and delayeds asfunctions of singles, determined from a phantom study, to the patientdata point as described previously for NECR and SNR. For any fixedobject position and emitter distribution, (P−D) and D are simplefunctions of the singles rate, s, that depend on the object only throughthe scale factors C^(T) and C^(R):P−D=C ^(T) sF ^(T)(s); andD=C ^(R) sF ^(R)(s),where F^(T)(s) and F^(R)(s) are object-independent live time functionsthat are very similar to the functions ƒ^(T)(s) and ƒ^(R)(S),respectively, that are used to model T (or (T+S)) and R. The onlydifference is that here, (P−D) and D refer to total counts rather thanthose in some other ROI. To the extent that this approximation isaccurate, PNECR(s) is predictable for the patient data.

FIG. 10 illustrates a comparison between P, (P−D) and D for the threephantom count rate studies on the LSO PET/CT described above andgraphically illustrated in FIG. 9. (P−D) and D have been independentlyscaled to match the NEMA 2001 count rate curves. The prompts shown areC^(T)(P−D)+C^(R)D after this scaling. As shown, the agreement betweenthe net trues and delayeds curves for these three very differentphantoms is quite good. Accordingly, the net trues and delayeds countrate curves are fit to the patient data by simple scaling. From this,PNECR(s) is computed. It is not essential to the present invention thatthe NEMA 2001 phantom be used as the reference scan. Other phantoms areuseful for providing an accurate match for net trues and delayeds inpatient data, and may be used to generate the model (P−D)(s) and D(s)curves within the spirit of the present invention.

A continuous representation of the model curves of (P−D) and D above isobtained by fitting appropriate functional forms to the phantom data. Anaverage PNECR(s) is then computed for a set of patient scans by a leastsquare fit of C^(T) and C^(R) to the data. More significantly, PNECR(s)is also computed for each bed position for which the coincidence ratesare evaluated at the patient's singles rate. The actual measured PNECRpoint will fall on this curve, and its deficit relative to the peakPNECR value is then determined. Since for a single patient and bedposition the scatter fraction is fixed, the ratio of actual to peakPNECR accurately reflects the NECR deficit as well. Further, the peakPNECR, unlike the measured PNECR, is largely independent of the activitypresent in the patient, and hence of the dose and uptake period.Accordingly, the peak PNECR is also a useful quantity to correlate withother factors, such as patient weight, that affect data quality.

Knowing the peak singles rate, defined as the singles rate at the peakPNECR, compared to the measured singles rate, the difference in theactivity present in the patient that would have been necessary toachieve peak performance is predicted. The transformation from singlesrate to activity is based on the reference phantom scan. That ratio ofactivity A in the phantom at the patient's peak singles rate to thephantom activity at the measured singles rate in the patient gives acorrection factor for the patient's activity as:

$\frac{A_{peak}^{patient}}{A_{actual}^{patient}} = {\frac{A^{phantom}( s_{peak}^{patient} )}{A^{phantom}( s_{actual}^{patient} )}.}$

This activity ratio, as in the case using SNR(D) described above, isapplied to the actual injected dose to predict the optimal dose. Theoptimal dose is then decay corrected to a standard uptake period such asone hour. The optimal dose is not sensitive to the elimination of partof dose, so long as the eliminated fraction remains constant.

FIG. 11 illustrates a comparison of net trues and delayeds count ratesmeasured for 93 bed positions in 15 patient studies on an ACCEL, withthe fitted model curves from a NEMA 2001 count rate test. In thisillustration, C^(T)=0.84 and C^(R)=1.03. The prompts curve is the sum ofthe scaled net trues and delayeds curves. Only ¹⁸F-FDG whole-bodystudies were included. The patient weight range was 54-109 kg, with anaverage and standard deviation of 79±16 kg. The injected doses rangedfrom 444 to 640 MBq, with an average and standard deviation of 555±53MBq. The uptake periods to the start of the first bed position variedfrom 39 to 111 min, with an average and standard deviation of 59±17 min.From the fitted net trues and delayeds curves, an average PNECR for thedata set is predicted as defined above. This is shown in FIG. 12together with the actual PNECR for each bed position, and the PNECRcurve for the NEMA 2001 reference phantom. On average the patient scanshad somewhat lower PNECR than could have been achieved on the machine,possibly indicating the need for higher injected doses.

A more powerful analysis is made by considering the PNECR curvecorresponding to each individual acquisition. FIG. 13 illustrates theactual and average patient PNECR of a set of 17 clinical whole-bodystudies comprising 84 bed positions on a BGO PET/CT. The patient weightrange was 57-100 kg, with an average and standard deviation of 81±12 kg.The injected doses ranged from 271 to 400 MBq, with an average andstandard deviation of 354±35 MBq. The uptake periods varied from 60 to95 min, with an average and standard deviation of 75±13 min. Alsoillustrated is the PNECR curve for a single one of the acquisitions forthe heaviest patient in this group. The point 18 corresponding to thisacquisition is outlined with a diamond shape in this and succeedingfigures.

For each individual PNECR curve, the maximum value is computed andplotted in FIG. 14 as a function of patient's weight. These values arelargely independent of the magnitude of the dose given the patient. FIG.14 illustrates a decrease in this peak PNECR with increasing patientweight. The linear correlation coefficient between the peak PNECR andweight for this patient sample is −0.51. The linear regression line isshown as a solid line.

The trend of peak PNECR count rate versus weight shown in FIG. 14 isused to estimate the scan duration needed to acquire an equal number ofpseudo-noise equivalent counts at each weight, which is proportional tothe reciprocal of the count rate. This is illustrated in FIG. 15normalized to unit scan time at 70 kg. True NECR, if available, mightimply an even steeper trend due to variation in the scattercontribution. Nevertheless, the result illustrated in FIG. 15 suggeststhat a 100 kg patient should be scanned at least 25% longer than a 70 kgpatient to achieve equivalent data SNR on this machine. The estimate ofFIG. 15 does not account for bed-to-bed variations for a given patient,or variations in scatter fractions.

The ratio of actual to maximum PNECR for individual acquisitions versuspatient weight is illustrated in FIG. 16. This ratio is not sensitive tothe scatter fraction, and should closely resemble an NECR ratio. All ofthe acquisitions shown were acquired at approximately 80% or greater oftheir peak NECR. A higher performance ratio is generally seen for thelighter patients, although certain acquisitions in even the heaviestpatients are close to optimal.

Based on knowledge of the singles rate at the peak PNECR, the ratio ofthe patient's activity at the time of the scan to that which would havebeen required to achieve maximum performance is estimated. Again, thisdoes not depend strongly on the scatter fraction. These ratios areillustrated in FIG. 17 as a function of weight. This ratio varies withbed position for a given patient. These ratios varied from 0.4 to 1.1for the 89 acquisitions examined. These activity ratios are also used topredict the dose of ¹⁸F-FDG that would have been required to achievethis peak count rate. This does is illustrated in FIG. 18. Theillustrated doses are decay corrected to an hour prior to eachindividual acquisition. The linear correlation coefficient between doseand weight here is 0.19.

From the foregoing description, it will be recognized by those skilledin the art that a new methodology for analyzing count rate performanceof clinical PET data has been provided. In the method of the presentinvention, either the net trues and delayed coincidence rates, or thetrues and randoms rates, if they were measured on patients as functionsof qualified single event rates, are proportional to the correspondingtrends measured in a reference phantom such as the NEMA 2001 70 cmcylinder. Therefore, a performance curve is estimated for each bedposition of each whole-body scan, and the location of the actualacquisition on this curve is determined. The appropriate adjustments toscan duration and injected dose are then determined to best utilizecount rate performance. The method of the present invention provides forthe use of either of SNR, NECR, or PNECR as a meaningful measure ofrelative performance. SNR may be defined either globally or locally.

Performance metrics other than SNR, NECR and PNECR may also be employedin the method of the present invention. For example, the randoms/truesratio, the live time ratio of T(s) to the linearly extrapolated T, andthe trues rate are each useful with the present invention.

While the present invention has been illustrated by description ofseveral embodiments and while the illustrative embodiments have beendescribed in considerable detail, it is not the intention of theapplicant to restrict or in any way limit the scope of the appendedclaims to such detail. Additional advantages and modifications willreadily appear to those skilled in the art. The invention in its broaderaspects is therefore not limited to the specific details, representativeapparatus and methods, and illustrative examples shown and described.Accordingly, departures may be made from such details without departingfrom the spirit or scope of applicant's general inventive concept.

1. A method for improving data quality in Positron Emission Tomography(PET), said method comprising the steps of: (a) determining a genericfunctional form T(p) for a true count rate response in a PET scanner,wherein p is a selected parameter; (b) determining a generic functionalform R(p) for a randoms count rate response in the PET scanner; (c)determining a value of a true count rate T in a specific clinicalpatient scan; (d) determining a value of a randoms count rate R in thespecific clinical patient scan; (e) determining a value of a selectedparameter p in the specific clinical patient scan; (f) calibrating saidgeneric functional form of T(p) using said values of T and p to acquirea calibrated T_(pat)(p), whereby said calibrated T_(pat)(p) accuratelyrepresents an actual count rate response for the patient and scanconfiguration; and (g) calibrating said generic functional form of R(p)using said values of R and p to acquire a calibrated R_(pat)(p), wherebysaid calibrated R_(pat)(p) accurately represents an actual count rateresponse for the patient and scan configuration.
 2. The method of claim1 further comprising the step of: (h) determining data quality metricsrelative to the patient and scan configuration, said step of determiningdata quality metrics being accomplished using at least one of saidT_(pat)(p) and said R_(pat)(p).
 3. The method of claim 1 wherein p is adirectly acquired quantity used to provide a count loss correction in aPET tomograph.
 4. The method of claim 1 wherein p is a singles eventrate in a PET tomograph, said singles event rate being selected from anintegral singles event rate and a vector comprising an individualdetector single event rates.
 5. The method of claim 4 wherein saidrandoms rate is estimated using one of a group of methods including atleast estimating said randoms rate directly from a delayeds sinogram,estimating said randoms rate as a fraction of a total delayeds rateassuming a uniform distribution and using an attenuation mask, andestimating said randoms rate from a spatial distribution of said singlesevent rate.
 6. The method of claim 1 wherein p is output from devicemeasuring detector dead time.
 7. The method of claim 6 wherein saiddevice measuring detector dead time is a live-time clock.
 8. The methodof claim 1 further including the step of: (i) determining a calibratedscatter count rate S_(pat)(p), said step of determining a scatter countrate S_(pat)(p) including the steps of: (1) determining a value of ascatter fraction S_(f) in the specific clinical patient scan by:S _(f) =S/(T+S); and (2) applying said scatter fraction value toT_(pat)(p) according to:S _(pat)(p)=[S _(f)/(1−S _(f))]T _(pat)(P).
 9. The method of claim 1further comprising the step of: (j) determining a true plus scattercount rate (T+S)(p), said step of determining a true plus scatter countrate including the steps of: (1) determining a generic functional form(T+S)(p) for count rate response; (2) determining a particular value for(T+S) in said specific clinical patient scan; and (3) calibrating saidgeneric functional form of (T+S)(p) using said particular values of(T+S) and said selected parameter p to acquire a calibrated (T+S)_(pat)(p), whereby said calibrated (T+S)_(pat)(p) accurately represents anactual count rate response for the patient and scan configuration. 10.The method of claim 9 wherein T(s) closely approximates (T+S)(s) inshape and wherein (T+S) defines a net trues rate, wherein (T+S) ismeasured directly, and wherein said trues rate is estimated bysubtracting an estimate of a mean scatter distribution.
 11. The methodof claim 9 further comprising the step of: (k) determining data qualitymetrics relative to the patient and scan configuration, said step ofdetermining data quality metrics being accomplished using at least oneof a scatter count rate S_(pat)(p) and said true plus scatter count rate(T+S)_(pat)(p) in conjunction with at least one of said true count rateT_(pat)(p) and said randoms count rate R_(pat)(p).
 12. The method ofclaim 11 wherein T_(pat)(p) is computed from T_(phant)(p) by calibratingwith T_(pat)(p_(pat) ^(meas)) according to:${{T_{pat}(p)} = {\frac{T_{pat}( p_{pat}^{meas} )}{T_{phant}( p_{pat}^{meas} )}{T_{phant}(p)}}};$and R_(pat)(p) is computed from R_(phant)(p) by calibrating withR_(pat)(p_(pat)^(meas)) according to:${R_{pat}(p)} = {\frac{R_{pat}( p_{pat}^{meas} )}{R_{phant}( p_{pat}^{meas} )}{{R_{phant}(p)}.}}$13. The method of claim 11, in said step of (k) determining data qualitymetrics relative to the patient and scan configuration, wherein saiddata quality metrics include at least one of a noise equivalent countrate NECR determined according to:${{NECR} = \frac{T^{2}}{T + S + {kR}}};$ a pseudo-noise equivalent countrate PNECR determined according to:${{PNECR} = \frac{( {T + S} )^{2}}{T + S + {( {{k/2} - 1} )R}}};$and a signal-to-noise ratio SNR determined according to:SNR=√{square root over (NECRt)} where k has a value between 1 and 2, andt is a scan duration.
 14. The method of claim 11, in said step of (k)determining data quality metrics relative to the patient and scanconfiguration, wherein said data quality metrics include at least one ofan optimal noise equivalent count rate NECR, an optimal pseudo-noiseequivalent count rate PNECR, an optimal signal-to-noise S ratio SNR, anoptimal injected dose, a dose deficit, an SNR deficit, an NECR deficit,a PNECR deficit, and a differential dose benefit.
 15. The method ofclaim 11 further comprising the step of developing a database of saiddata quality metrics relating patient characteristics including at leastweight, body mass index, sex, disease, diabetes state, and anatomicalposition to optimal dose and peak SNR.
 16. The method of claim 15further including the step of statistically correlating said optimaldose for each scan completed into said database.
 17. The method of claim15 further including the steps of: (a) comparing said patientcharacteristics for a new patient with said database; and (b) estimatingsaid optimal dose for said new patient.
 18. The method of claim 9wherein at least one of said steps of determining a generic functionalform T(p); determining a generic functional form R(p); and determining ageneric functional form (T+S)(p) is performed using at least onemeasurement on a phantom to acquire T_(phant)(p), R_(phant)(p) and(T+S)_(phant)(p), respectively.
 19. The method of claim 18 wherein(T+S)_(pat)(p) is computed from (T+S)_(phant)(p) by calibrating with(T + S)_(pat)(p_(pat)^(meas)) according to:${( {T + S} )_{pat}(p)} = {\frac{( {T + S} )_{pat}( p_{pat}^{meas} )}{( {T + S} )_{phant}( p_{pat}^{meas} )}( {T + S} )_{phant}(p)}$20. The method of claim 9 wherein said true count rate T, said randomscount rate R, a scatter count rate S, said true and scatter count rateT+S, said true count rate response function T(p), said randoms countrate response function R(p), said scatter count rate response functionS(p), and said true and scatter count rate response function (T+S)(p)refer to count rates selected from integral count rates and local countrates determined from weighted sums over particular regions of interestin available data, said available data being distributed in at least oneof space, energy and time.
 21. The method of claim 9 further comprisingthe step of: (1) repeating said steps of (f) calibrating said genericfunctional form of T(p) using said values of T and p to acquire acalibrated T_(pat)(p); (g) calibrating said generic functional form ofR(p) using said values of R and p to acquire a calibrated R_(pat)(p);and (j)(3) calibrating said generic functional form of (T+S)(p) usingsaid particular values of (T+S) and said selected parameter p to acquirea calibrated (T+S)_(pat)(p) to acquire said T_(pat)(p), R_(pat)(p),and(T+S)_(pat)(p), respectively, corresponding to distinct regions ofinterest.
 22. The method of claim 9 wherein said step of (f) calibratingsaid generic functional form of T(p) using said values of T and p toacquire a calibrated T_(pat)(p) includes the steps of: (1) selectingsaid selected parameter p to be monotonically variable with respect toactivity A_(pat) potentially present in the patient; (2) determining ageneric functional form p(A) using at least one of at least onemeasurement on a phantom and theoretical considerations; (3) invertingsaid p(A) to determine a generic functional form A(p); (4) determining avalue of A in a specific clinical patient scan, wherein A represents atleast a quantity proportional to the actual total activity present; (5)calibrating said generic functional form of A(p) using said value of Ato acquire a calibrated A_(pat)(p) according to:${{A_{pat}(p)} = {\frac{A_{pat}( p_{pat}^{meas} )}{A_{phant}( p_{pat}^{Meas} )}{A_{phant}(p)}}};$(6) inverting A_(pat)A(p) to determine p(A_(pat)); and (7) substitutingp(A_(pat)) into T(p) to acquire T(p(A_(pat))); wherein said step of (g)calibrating said generic functional form of R(p) using said values of Rand p to acquire a calibrated R_(pat)(p), includes the step of: (8)substituting p(A_(pat)) into R(p) to acquire R(p(A_(pat))); and whereinsaid step of (j)(3) calibrating said generic functional form of (T+S)(p)using said values of (T+S) and p to acquire a calibrated (T+S)_(pat)(p),includes the step of: (9) substituting p(A_(pat)) into (T+S)(p) toacquire (T+S)(p(A_(pat))).
 23. The method of claim 22 wherein saidactivity A_(pat) is a dose D_(inj) of radiopharmaceutical injected inthe patient, D_(inj) being calibrated to said generic form A(p)according to:${D_{inj}(p)} = {\frac{D_{inj}( p_{pat}^{meas} )}{A_{phant}( p_{pat}^{Meas} )}{{A_{phant}(p)}.}}$24. The method of claim 23 further comprising the step of correctingsaid injected dose D_(inj) for at least one of decay correction to astandard uptake period and for excretion.
 25. The method of claim 1,before said step of (a) determining a generic functional form T(p) for atrue count rate response, further comprising the steps of: (aa)injecting a patient with a calibration dose of a radiopharmaceutical,said calibration dose being a fractionated portion of a patient dose ofthe radiopharmaceutical; and (ab) pre-scanning the patient; and aftersaid step of (g) calibrating said generic functional form of R(p),further comprising the steps of: (h) determining a calibrated true plusscatter count rate (T+S)_(pat)(p); (i) determining an optimal dose ofthe radiopharmaceutical; (j) determining a remainder dose as adifference between said optimal dose and said calibration dose; and (k)injecting said patient with said remainder dose.